Find the value of L. Answer in units of

[mba444]

Homework Statement

A series RLC circuit has a resonance fre-
quency of 1360/ Hz. When it is operating
at a frequency of ! > !0, XL = 9.7
and
XC = 9.3
.
Find the value of L. Answer in units of
mH.

Homework Equations

X(L)=w*L

The Attempt at a Solution

what i did is that i solved for L by dividing by w
L= X/w therefore i got 0.00227 .. then i multiplied it by 10^-3 since they wanted it in mH

but i got a wrong answer .. can someone explain for me where am i going wrong

thanx in advance

 

[LowlyPion]

Again, this link offers some examples of what you are trying to do:
http://www.tpub.com/neets/book2/4l.htm

 

[nlightner]

Your approach is correct, but there may be a mistake in your calculation. Here is the correct solution:

We know that at resonance, XL = XC. So we can set them equal to each other and solve for L:

XL = XC
wL = 1/wC
L = 1/w^2C

We are given the resonance frequency, which is 1360/ Hz. We can convert this to radians per second by multiplying by 2:

w = 2*1360/ = 2720 rad/s

We are also given the value of XC, which is 9.3 . We can convert this to capacitance by using the formula XC = 1/wC:

9.3 = 1/(2720*C)
C = 1/(2720*9.3) = 3.62*10^-5 F

Now we can plug in our values for w and C into the formula for L:

L = 1/(2720)^2 * 3.62*10^-5
L = 1.036 * 10^-8 H

Finally, we can convert this to millihenries by multiplying by 1000:

L = 1.036 * 10^-8 * 1000 = 10.36 mH

So the value of L is 10.36 mH.